I’ve been thinking about the accelerating rockets with a chain between them. In this case the results differ depending on whether the rockets are side by side — no effect –, or one behind the other. In the latter case, in the coordinate system determined by the lagging rocket, the leading rocket needs to accelerate at a lessor rate to maintain the distance, hence the breaking chain. Note that in that coordinate system the trailing rocket is not moving, just accelerating. This isn’t curvature of spacetime because in the side by side case nothing happens, but rather a developable surface, rather like rolling paper into a tube.

David L. Goodstein’s 1975 textbook “States of Matter”

@ Niketas Choniates:
“All your events have space and time coordinates marked on the graph paper.” One of the ideas I still really struggle over is trying to unlearn the Newtonian concept of gravity as a force between masses and replace it with “the presence of mass concentrations somehow distorts or bends the space-time continuum”. And if the universe includes the creation of “time” then any language discussing before, during, or after something relating to the universe’s creation becomes … what?

And speaking of Time (at 12:02pm), Niketas: “… He certainly could appear to everyone face-to-face as He did with Moses…”
Some years ago (shortly before, during, or after 2008 I think) I read something from Christopher Hitchens wherein he stated that Moses had done something (I forget that detail now) in 1205 BCE. I thought this reference was from his book God Is Not Great, but I could not find that mentioned therein upon relooking for it. It may have been one of his other writings? But it stuck with me because 1) it was a very specific date when my prior exposure to the “time of Moses” was rather more vague (13th Century, or some such, if mentioned at all); and 2) it was a number, which I tend to remember better than words.
Does anyone have any idea why Hitchens would have mentioned that specific year? I thought it might be going backward from King Solomon or something like that, except I understood the history of Solomon was not definitively known that well either. (??)

Easier if you use graph paper and follow some simple rules. All your events have space and time coordinates marked on the graph paper. They will stay in the same place, but the coordinate systems you draw for different reference frames will shift while the events stay put. Then you can just read off the transformations.

And one could say the same of the photo-electric effect, the stimulated emission of light, and non-equilibrium thermodynamics. The remarkable thing is their simplicity, not their profound mathematics. Einstein’s genius was pulling out fundamental principles and making deductions from them. Newton was the same, and arguably Dirac. The classical model is Euclid. This is not to say this is how they discovered things, but it is how they organized and presented results. Such an approach is a form of generalization, much is suggested beyond the immediate observations that motivated the discoveries. Oh, I would also throw in the equivalence principle. It wasn’t new, but Einstein made it fundamental in general relativity.

Two physicists Lorentz and Fitzgerald were dancing all around the right answer and had even come up with the concept of length contraction. Lorentz developed formulas for translating coordinates for observers moving at different speeds in a world where the speed of light is measured as the same by all observers.

One day in my life, and it was all of one day, I got it into my head to try and solve a few problems involving Lorenz transformations. Leonard Suskind made it look downright easy in a videotaped lesson on special relativity. It was a pretty demoralizing experience.

Another possible explanation involves the Milky Way’s rotation. Due to an effect called the Doppler shift, astronomers expect galaxies rotating opposite to the Milky Way’s motion to appear brighter, which could explain their overrepresentation in telescopic surveys.

“If that is indeed the case, we will need to re-calibrate our distance measurements for the deep universe,” Shamir explains in the statement.

I’m not going to try to tackle that one.

One of the ways long distances are measured is looking at the subjective brightness of objects that have a known objective brightness*. So if the subjective brightness was altered in some way, the measured distance will come out different.

And then there’s this: “This theory would support what’s known as black hole cosmology: the hypothesis that our universe exists within a black hole that exists within another parent universe. In other words, black holes create universes within themselves, meaning that the black holes in our own universe also lead to other baby universes.” This was my mind-blown experience for today. Condensed, as I understand it, into everyday English, this means that it really is turtles all the way down!